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Maths Quest A Year 11 for Queensland WorkSHEET 10.2 Chapter 10 Describing, exploring and comparing data WorkSHEET 10.2 1 Describing, exploring and comparing data Name: ___________________________ 1 The following data show the survey results of the number of children in families. No of children 1 2 3 4 5 6 Total Data: 3, 5, 2, 4, 3, 1, 4, 1, 2, 5, 3, 6, 4, 3, 5, 4, 4. Create a frequency table for this data. 2 Tally ll ll llll llll lll l Frequency 2 2 4 5 3 1 17 Using the frequency table from question 1 find: (a) ( 2 1) ( 2 2) ( 4 3) (5 4) (3 5) (1 6) (a) the mean number of children per family 17 59 17 3.47 (b) the median number of children per family (c) the modal number of children per family 3 Lachlan has calculated his mean mathematics score to be 67%, based on eight tests. If he scores 75% on the ninth test, what will his new mean score be? (b) 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, Median = 4 (c) Mode = 4 (67 8) 75 611 9 9 67.88 Lachlan’s new mean score will be 68%. Maths Quest A Year 11 for Queensland 4 Chapter 10 Describing, exploring and comparing data A shoe company surveyed the shoe size purchased by women over a period of time. The results were as follows: WorkSHEET 10.2 2 (a) 85 6 58 6 7 9 5 7 6 88 69 7 8 17 8, 5, 6, 5, 8, 6, 7, 9, 5, 7, 6, 8, 8, 6, 9, 7, and 8. 5 (a) Calculate the mean of this data (b) Find the modal value. (c) Find the median value. (d) Which of these values would be of the most use to the company? Why? 118 17 6.94 The mean shoe size is 7. Tom has been earning some extra pocket money by washing cars. In each hour block he has managed to wash 4 cars, 5 cars, 3 cars, 4 cars and 4 cars. The mean number of cars that he has been able to wash is therefore 4 cars per hour. (b) The mode is 8 (c) 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, The median value is 7. (d) The mode would probably be of the most value because this is the shoe size that they sell the most. 45344 x 6 20 x 6 20 x x 5 5 30 10 In order to increase his mean to 5 cars per hour, Tom needs to wash 10 cars in his next hour. how many cars does Tom need to wash in the No, this is not very likely. next hour? Is this likely? 6 This grouped frequency table gives the number of ‘salmon cod’ caught by a fisherman on 25 fishing trips. Number of Frequency f salmon cod 20–24 1 25–29 2 30–34 4 35–39 4 40–44 6 45–49 8 Add a cumulative frequency column to the table, then use this to determine the median class. 4 Number of Frequency f salmon cod Cumulative frequency 20–24 1 1 25–29 2 3 30–34 4 7 35–39 4 11 40–44 6 17 45–49 8 25 25 1 th score 2 13th score Median class is 40 44. Median Maths Quest A Year 11 for Queensland 7 Chapter 10 Describing, exploring and comparing data Use the frequency distribution table in questions 6 to calculate the mean number of ‘salmon cod’ caught by the fisherman on his 25 fishing trips. WorkSHEET 10.2 Class Frequency Number of salmon cod centre (x ) f fx 20–24 22 1 22 25–29 27 2 54 30–34 32 4 128 35–39 37 4 148 40–44 42 6 252 45–49 47 8 f 25 3 376 fx 980 fx f 980 25 39.2 x 8 From the distribution table in question 6, determine the modal class. 9 The number of goals scored by a team is shown below: 5, 4, 4, 7, 5, 9, 12, 14, 16, 16. modal class = 45 – 49 cod. 2 4, 4, 5, 5, 7, 9, 12, 14, 16, 16 LQ (a) Find the lower quartile. 10 median UQ (b) Find the upper quartile. (a) Lower quartile = 5 (c) Find the interquartile range. (b) Upper quartile = 14 (c) Interquartile range = 14 5 =9 Use your calculator to find the standard deviation of the set of outcomes when a six-sided die is rolled as shown below. 1, 2, 3, 4, 5, 6 State your answer correct to two decimal places. 1 Standard deviation = 1.87